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sammy [17]
3 years ago
11

Find the measure of angle x in the figure below: Two triangles are shown such that one triangle is inverted and they share a com

mon vertex. The lower triangle has two angles at the base. The lower left angle is marked as 45 degrees. The lower right angle is marked as 55 degrees. The angle at the vertex of the inverted triangle at the top is marked as x degrees. The angle at the vertex of the bottom triangle is marked as y degrees. 45° 80° 55° 100°
Mathematics
1 answer:
vlabodo [156]3 years ago
7 0
Y can be found by setting the 3 angles in the bottom triangle equal to 180 degrees like so:

45 + 55 + y = 180

100 + y = 180 (Simplify)

y = 80 (Subtract 100 from both sides)

Angles x and y are opposite angles, so they are equal to each other. This means that x = 80 degrees also.
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Use the drawing below to answer the questions that follow.
zhannawk [14.2K]

you have to multiple 16 i think

8 0
2 years ago
Read 2 more answers
Find the distance between the point (-2, -3) and the line with the equation y=4-2/3x
otez555 [7]

Answer:

D = \frac{25\sqrt{13}}{13}

Step-by-step explanation:

Given

y = 4 - \frac{2}{3}x

(x_1,y_1) = (-2,-3)

Required

Determine the distance

y = 4 - \frac{2}{3}x

Write the above equation in standard form:

Ax + By + C = 0

So, we have:

\frac{2}{3}x+y  - 4 = 0

By comparison:

A = \frac{2}{3}  B = 1 and C = -4

The distance is calculated using:

D = \frac{|Ax_1 + By_1 + C|}{\sqrt{A^2 + B^2}}

Where:

(x_1,y_1) = (-2,-3)

A = \frac{2}{3}  B = 1 and C = -4

This gives:

D = \frac{|\frac{2}{3} * (-2) + 1 * (-3) - 4|}{\sqrt{(\frac{2}{3})^2 + 1^2}}

D = \frac{|-\frac{4}{3} -3 - 4|}{\sqrt{\frac{4}{9} + 1}}

Take LCM

D = \frac{|\frac{-4-9-12}{3}|}{\sqrt{\frac{4+9}{9}}}

D = \frac{|\frac{-25}{3}|}{\sqrt{\frac{13}{9}}}

D = |\frac{-25}{3}|/\sqrt{\frac{13}{9}}

D = \frac{25}{3}/\sqrt{\frac{13}{9}}

Split the square root

D = \frac{25}{3}/\frac{\sqrt{13}}{\sqrt{9}}

Change / to *

D = \frac{25}{3}*\frac{\sqrt{9}}{\sqrt{13}}

D = \frac{25}{3}*\frac{3}{\sqrt{13}}

D = \frac{25}{\sqrt{13}}

Rationalize

D = \frac{25}{\sqrt{13}} * \frac{\sqrt{13}}{\sqrt{13}}

D = \frac{25\sqrt{13}}{13}

Hence, the distance is:

D = \frac{25\sqrt{13}}{13}

4 0
3 years ago
Find X please.......
nikdorinn [45]
So Angle 5 = 1x - 7 and angle 2 = -2x + 18. You can work out that angle 1 is the same as angle 5 because corresponding angles are equal. Then you know that angle 1 + angle 2 = 180 because angles on a straight line add to 180. So therefore 1x - 7 -2x + 18 = 180 so -1x + 11 = 180 so -x = 169 so x = -169. Hope this helps :)
8 0
3 years ago
Question 1: Explain how the letter x (or any letter) is used when writing expressions, and give an example. How are expressions
BaLLatris [955]

Answer:

Question 1:

The letter x or any letter used when writing an expression is representative of  unit of an idea, quantity or measure, such that it can be translated in the expression to provide information about a related idea

Question 2:

The expression can be translated as two times the expression three (variable) x minus two (variable) y plus the constant 7

Question 3:

In the first expression, the like terms are;

10y and (-2y),

3x and x

In the second expression, the like terms are;

-y and -2y

3x and 4x

The first expression simplifies to 8y + 4x + 10

The second expression simplifies to  7x - 3y + 6

Question 4:

The expression is evaluated as 122

Question 5:

The equivalent expression of the expression 3(4x + 2y) + 5x, is 17x + 6y

To prove when x = 1 and y = 2 we have;

3(4×1 + 2×2) + 5×1 is 29

17×1 + 6×2 is 29 which are equivalent in value

Step-by-step explanation:

Question 1:

The letter x or any letter used when writing an expression is representative of  unit of an idea, quantity or measure, such that it can be translated in the expression to provide information about a related idea

Example;

If x is the symbol representing the average number of oranges sold in 1 hour, then the expression for the number of oranges sold per day of 24 hours  = 24·x

An expression is a written mathematical symbolic statement that shows the the finite merging together of representative symbols by the mathematical operations that govern the present constraints

An equation is a statement that two expressions are equal

Question 2:

The given expression is 2(3x - 2y) + 7

The parts are;

The coefficient of (3x - 2y) = 2

The constant term = 7

The variables are x and y

Which gives

The coefficient of the variable x = 6

The coefficient of the variable y = -4

The expression can be translated as two times the expression three (variable) x minus two (variable) y plus the constant 7

or

The expression can be translated as two times the bracket open three times (variable) x minus two times (variable) y bracket close plus the constant 7

or

The expression can be expanded as 2(3x - 2y) + 7 → 6·x - 4·y + 7 which is expressed verbally as follows;

Six times (variable) x minus four times (variable) y plus the constant 7

Question 3:

The expressions are;

10y + 3x + 10 + x  - 2y..........................(1)

3x - y + 4x + 6 - 2y,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,(2)

In the first expression, the like terms are;

10y and (-2y),

3x and x

In the second expression, the like terms are;

-y and -2y

3x and 4x

They are like terms because they can be simply added together to simplify the expressions as follows

10y + 3x + 10 + x  - 2y gives 10y - 2y + 3x + x  10  to give 8y + 4x + 10

Also

3x - y + 4x + 6 - 2y  gives  3x+ 4x - y  - 2y + 6 to give 7x - 3y + 6

Question 4:

The expression 8x² + 25·y when x = 3 and y = 2 is evaluated by replacing (putting) the value x and y (into the expression)

The expression is then evaluated as 8×3² + 25×2 which is the same as 72 + 50 or 122

Question 5:

To write the equivalent expression of the expression 3(4x + 2y) + 5x, we expand the expression as follows;

3×4x + 3×2y + 4x which is 12x + 6y + 4x

We combine like terms;

12x + 5x + 6y which is 17x + 6y

To prove we can check by substituting a value for each of the variables x and y such as x = 1 and y = 2

3(4×1 + 2×2) + 5×1 is 29

17×1 + 6×2 is 29

5 0
3 years ago
HELP ASAP! Please give a detailed explanation!
mash [69]

Answer:

If the first die is a 5, the second must be 5 or more in order to have a sum of at least ten.

Assuming it is a six sided die, the two values that would make this true are 5 and 6.

2 values/6 possible would be a probability of 2/6, which simplifies to 1/3

Final answer: 1/3

Step-by-step explanation:

6 0
3 years ago
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